Extended depth of focus (EDOF) lens to increase pseudo-accommodation by utilizing pupil dynamics

ABSTRACT

In one aspect, the present invention provides an ophthalmic lens (e.g., an IOL) that includes an optic having an anterior surface and a posterior surface disposed about an optical axis. At least one of the surfaces (e.g., the anterior surface) has a profile characterized by superposition of a base profile and an auxiliary profile. The auxiliary profile can include an inner region, an outer region and a transition region between the inner and the outer regions, where an optical path difference across the transition region (i.e., the optical path difference between the inner and the outer radial boundaries of the transition region) corresponds to a non-integer fraction (e.g., ½) of a design wavelength (e.g., a wavelength of about 550 nm).

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.12/503,267 filed on Jul. 15, 2009, now U.S. Pat. No. 8,241,354 whichclaims priority to U.S. Provisional Application No. 61/080,790 filed onJul. 15, 2008, both of which are incorporated herein by reference.

BACKGROUND

The present invention relates generally to ophthalmic lenses, and moreparticularly, to intraocular lenses (IOLs) that provide enhanced visionvia controlled variation of the phase shift across a transition regionprovided on at least one of the lens surfaces.

Intraocular lenses (IOLs) are routinely implanted in patients' eyesduring cataract surgery to replace the natural crystalline lens. Theoptical power of the natural crystalline lens can vary under theinfluence of the ciliary muscles to provide accommodation for viewingobjects at different distances from the eye. Many IOLs, however, providea monofocal power with no provision for accommodation. Mutlifocal IOLsare also known that provide a distance optical power as well as a nearoptical power (e.g., by employing diffractive structures), therebyproviding a degree of pseudoaccommodation.

There is, however, still a need for improved IOLs that can providepseudo-accommodative optical power while providing sharp optical imagesover a wide range of pupil sizes. In designing IOLs and lensesgenerally, optical performance can be determined by measurements using aso-called “model eye” or by calculations, such as predictive raytracing. Typically, such measurements and calculations are performedbased on light from a narrow selected region of the visible spectrum tominimize chromatic aberrations. This narrow region is known as the“design wavelength.”

SUMMARY

In one aspect, the present invention provides an ophthalmic lens (e.g.,an IOL) that includes an optic having an anterior surface and aposterior surface disposed about an optical axis. At least one of thesurfaces (e.g., the anterior surface) has a profile characterized bysuperposition of a base profile and an auxiliary profile. The auxiliaryprofile can include at least two regions (e.g., an inner region and anouter region) and one or more transition regions between the regions,where an optical path difference across the transition region (i.e., theoptical path difference between the inner and the outer radialboundaries of the transition region) corresponds to a non-integerfraction (e.g., ½) of a design wavelength (e.g., a wavelength of about550 nm).

The transition region of the auxiliary profile can extend from an innerradial boundary to an outer radial boundary. In many embodiments, theinner radial boundary of the transition region corresponds to an outerradial boundary of the inner region and the outer radial boundary of thetransition region correspond to an inner radial boundary of the outerregion of the auxiliary profile. In many embodiments, the transitionregion can be adapted to provide a monotonic change in optical pathdifference relative to its inner radial boundary as a function ofincreasing radial distance from the optical axis. A monotonic change inthe optical path difference can be characterized by a continuousincrease or decrease as a function of radial distance, which in somecases is interspersed with regions of no change (plateau regions). Byway of example, the monotonic change can be characterized by a linearchange or by a succession of linear changes separated by one or moreplateaus.

In some embodiments, the profile (Z_(sag)) of the surface formed assuperposition of a base profile and an auxiliary profile can be definedby the following relation:Z _(sag) =Z _(base) +Z _(aux),wherein,

Z_(sag) denotes a sag of the surface relative to the optical axis as afunction of radial distance from that axis, and wherein,

${z_{base} = {\frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {a_{2}r^{2}} + {a_{4}r^{4}} + {a_{6}r^{6}} + \ldots}}\mspace{14mu},$wherein,

r denotes a radial distance from the optical axis,

c denotes a base curvature of the surface,

k denotes a conic constant,

a₂ is a second order deformation constant,

a₄ is a fourth order deformation constant,

a₆ is a sixth order deformation constant, and wherein,

$Z_{aux} = \left\{ \begin{matrix}{0,} & {0 \leq r < r_{1}} \\{{\frac{\Delta}{\left( {r_{2} - r_{1}} \right)}\left( {r - r_{1}} \right)},} & {r_{1} \leq r < r_{2}} \\{\Delta,} & {r_{2} < r}\end{matrix} \right.$wherein,

r₁ denotes an inner radial boundary of the transition region,

r₂ denotes an outer radial boundary of the transition region, and

wherein,

Δ is defined by the following relation:

${\Delta = \frac{\alpha\;\lambda}{\left( {n_{2} - n_{1}} \right)}},$wherein,

n₁ denotes an index of refraction of material forming the optic,

n₂ denotes an index of refraction of a medium surrounding the optic,

λ denotes a design wavelength (e.g., 550 nm), and

α denotes a non-integer fraction (e.g., ½).

In some other embodiments, the profile (Z_(sag)) of the lens surfacehaving the auxiliary profile can be defined by the following relation:Z _(sag) =Z _(base) +Z _(aux)wherein,

Z_(sag) denotes a sag of the surface relative to the optical axis as afunction of radial distance from that axis, and wherein,

${z_{base} = {\frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {a_{2}r^{2}} + {a_{4}r^{4}} + {a_{6}r^{6}} + \ldots}}\mspace{14mu},$wherein,

r denotes a radial distance from the optical axis,

c denotes a base curvature of the surface,

k denotes a conic constant,

a₂ is a second order deformation constant,

a₄ is a fourth order deformation constant,

a₆ is a sixth order deformation constant, and wherein,

$z_{aux} = \left\{ \begin{matrix}{0,} & {0 \leq r < r_{1a}} \\{{\frac{\Delta_{1}}{\left( {r_{1b} - r_{1a}} \right)}\left( {r - r_{1a}} \right)},} & {r_{{1a}\;} \leq r < r_{1b}} \\{\Delta_{1},} & {r_{1b} \leq r < r_{2a}} \\{{\Delta_{1} + {\frac{\left( {\Delta_{2} - \Delta_{1}} \right)}{\left( {r_{2b} - r_{2a}} \right)}\left( {r - r_{2a}} \right)}},} & {r_{2a} \leq r < r_{2b}} \\\Delta_{2} & {r_{2b} < r}\end{matrix} \right.$wherein

r denotes the radial distance from an optical axis of the lens,

r_(1a) denotes the inner radius of a first substantially linear portionof transition region of the auxiliary profile,

r_(1b) denotes the outer radius of the first linear portion,

r_(2a) denotes the inner radius of a second substantially linear portionof the transition region of the auxiliary profile, and

r_(2b) denotes the outer radius of the second linear portion, andwherein

each of Δ₁ and Δ₂ can be defined in accordance with the followingrelation:

${\Delta_{1} = \frac{\alpha_{1}\lambda}{\left( {n_{2} - n_{1}} \right)}},{and}$$\Delta_{2} = {\frac{\alpha_{2}\lambda}{\left( {n_{2} - n_{1}} \right)}.\mspace{14mu}{and}}$wherein,

n₁ denotes an index of refraction of material forming the optic,

n₂ denotes an index of refraction of a medium surrounding the optic,

λ denotes a design wavelength (e.g., 550 nm),

α₁ denotes a non-integer fraction (e.g., ½), and

α₂ denotes a non-integer fraction (e.g., ½).

By way of example, in the above relations, the base curvature c can bein a range of about 0.0152 mm⁻¹ to about 0.0659 mm⁻¹, and the conicconstant k can be in a range of about −1162 to about −19, a₂ can be in arange of about −0.00032 mm⁻¹ to about 0.0 mm⁻¹, a₄ can be in a range ofabout 0.0 mm⁻³ to about −0.000053 (minus 5.3×10⁻⁵) mm⁻³, and a₆ can bein a range of about 0.0 mm⁻⁵ to about 0.000153 (1.53×10⁻⁴) mm⁻⁵.

In another aspect, an ophthalmic lens (e.g., an IOL) is disclosed thatincludes an optic having an anterior surface and a posterior surfacedisposed about an optical axis. At least one of those surfaces includesat least one inner refractive region, at least one outer refractiveregion, and a refractive transition region that extends from an outerradial boundary of the inner region to an inner radial boundary of theouter region. The transition region is adapted such that a phase ofradiation incident thereon at a design wavelength (e.g., 550 nm) variesmonotonically from said inner radial boundary to said outer radialboundary so as to generate a phase shift between those boundaries thatis characterized by a non-integer fraction of that design wavelength.While in some cases the non-integer fraction is less than one, in othercases it is greater than one.

In some embodiments, the anterior and the posterior surfaces exhibitbase profiles adapted to impart a nominal refractive optical power,e.g., a power in a range of about −15 to about +50 Diopters, to thelens.

In a related aspect, the surface having the transition region can have aradial diameter in a range of about 1 mm to about 5 mm, and thetransition region can be in the form of an annular region having aradial width in a range of about 0 to about 1 mm.

In another aspect, in the above ophthalmic lens, the optic exhibits athrough-focus modulation transfer function that is asymmetric relativeto a focal plane of the optic for aperture sizes in a range of about 1.5mm to about 6 mm.

In another aspect, an ophthalmic lens (e.g., an IOL) is disclosed thatincludes an optic having an anterior surface and a posterior surfacedisposed about an optical axis, where each surface includes a basesurface profile. A pattern of surface variations are superimposed on thebase surface profile of at least one of the surfaces so as to generate atransition region extending between an inner and an outer surfaceregion. The transition region causes the optic to exhibit an asymmetricthrough-focus modulation transfer function of light incident on theoptic (e.g., light having a design wavelength (e.g., 550 nm)) through anaperture having a diameter in a range of about 1.5 mm to about 6 mm.

In some embodiments, the above lens can exhibit a depth of field in arange of about 0.25 Diopters to about 1.75 Diopters for light incidentthereon through an aperture having a diameter in a range of about 1.5 mmto about 6 mm for said design wavelength.

In some embodiments, the above lens can exhibit a substantiallysymmetric through-focus modulation transfer function for light at thedesign wavelength incident on the optic through an aperture having adiameter less than about 2 mm while exhibiting an asymmetricthrough-focus modulation transfer function for greater apertures. Insome cases, the optic exhibits a depth-of-field in a range of about 0.25D to about 1.75 D for light incident thereon through an aperture havinga diameter in a range of about 1.5 mm to about 6 mm for the designwavelength.

In another aspect, the invention provides an ophthalmic lens (e.g., anIOL), which comprises an optic having an anterior surface and aposterior surface, where each surface has a base profile such that theprofiles cooperatively impart a nominal optical power to the optic. Atleast one of the surfaces has a profile defined by addition of anauxiliary surface profile to its nominal surface profile, where theauxiliary profile is characterized by a central region, an outer regionand a transition region extending between the inner and the outerregions. The auxiliary profile is adapted to cause a shift between aneffective optical power and said nominal optical power for light havinga design wavelength and incident on the optic through an aperture havinga size in a selected range, e.g., a shift in a range of about 0.25 D toabout 1.75 D. The effective optical power can be characterized by thepeak of a through-focus modulation transfer function of the optic atsaid design wavelength and said aperture.

In a related aspect, in the above lens, the auxiliary profile is adaptedto enhance the depth of field of the optic.

In another aspect, an ophthalmic lens (e.g., an IOL), is disclosed thatincludes an optic having an anterior surface and a posterior surfacedisposed about an optical axis. At least one of the surfaces includes atleast an inner refractive region and at least an outer refractiveregion, where the profile of that surface is configured to impart amonotonically changing phase shift to incident radiation (e.g., incidentradiation at a design wavelength) from an outer boundary of the innerregion to an inner boundary of the outer region to provide a phase shiftbetween the two boundaries that is a non-integer fraction of a designwavelength (e.g., 550 nm). In some cases, the surface profile isconfigured such that the phase shift would occur over a radial distancein a range of about 0.75 mm to about 2.5 mm. Further, in some cases, thephase shift can effect an extension of the depth-of-focus exhibited bythe optic by a value in a range of about 0.25 D to about 1.75 D.

In a related aspect, the radial derivative of the profile of thatsurface at the outer boundary of the inner region exhibits adiscontinuity.

Further understanding of the invention can be obtained by reference tothe following detailed description and the accompanying drawings, whichare described briefly below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 A is a schematic cross-sectional view of an IOL according to anembodiment of the invention,

FIG. 1B is schematic top view of the anterior surface of the IOL shownin FIG. 1A,

FIG. 2A schematically depicts phase advancement induced in a wavefrontincident on a surface of a lens according to one implementation of anembodiment of the invention via a transition region provided on thatsurface according to the teachings of the invention,

FIG. 2B schematically depicts phase delay induced in a wavefrontincident on a surface of a lens according to another implementation ofan embodiment of the invention via a transition region provided on thesurface according to the teachings of the invention,

FIG. 3 schematically depicts that the profile of at least a surface of alens according to an embodiment of the invention can be characterized bysuperposition of a base profile and an auxiliary profile,

FIGS. 4A-4C provide calculated through-focus MTF plots for ahypothetical lens according to an embodiment of the invention fordifferent pupil sizes,

FIGS. 5A-5F provide calculated through-focus MTF plots for hypotheticallenses according to some embodiments of the invention, where each lenshas a surface characterized by a base profile and an auxiliary profiledefining a transition region providing a different Optical PathDifference (OPD) between an inner and an outer region of the auxiliaryprofile relative to the respective OPD in the other lenses,

FIG. 6 is a schematic cross-sectional view of an IOL according toanother embodiment of the invention, and

FIG. 7 schematically depicts that the profile of the anterior surfacecan be characterized as a superposition of a base profile and anauxiliary profile that includes a two-step transition region, and

FIG. 8 presents calculated through-focus monochromatic MTF plots for ahypothetical lens according to an embodiment of the invention having atwo-step transition region.

DETAILED DESCRIPTION

The present invention is generally directed to ophthalmic lenses (suchas IOLs) and methods for correcting vision that employ such lenses. Inthe embodiments that follow, the salient features of various aspects ofthe invention are discussed in connection with intraocular lenses(IOLs). The teachings of the invention can also be applied to otherophthalmic lenses, such as contact lenses. The term “intraocular lens”and its abbreviation “IOL” are used herein interchangeably to describelenses that are implanted into the interior of the eye to either replacethe eye's natural lens or to otherwise augment vision regardless ofwhether or not the natural lens is removed. Intracorneal lenses andphakic intraocular lenses are examples of lenses that may be implantedinto the eye without removal of the natural lens. In many embodiments,the lens can include a controlled pattern of surface modulations thatselectively impart an optical path difference between an inner and anouter portion of the lens's optic such that the lens would provide sharpimages for small and large pupil diameters as well aspseudo-accommodation for viewing objects with intermediate pupildiameters.

FIGS. 1A and 1B schematically depict an intraocular lens (IOL) 10according to an embodiment of the invention that includes an optic 12having an anterior surface 14 and a posterior surface 16 that aredisposed about an optical axis OA. As shown in FIG. 1B, the anteriorsurface 14 includes an inner refractive region 18, an outer annularrefractive region 20, and an annular transition region 22 that extendsbetween the inner and outer refractive regions. In contrast, theposterior surface 16 is in the form of a smooth convex surface. In someembodiments, the optic 12 can have a diameter D in a range of about 1 mmto about 5 mm, though other diameters can also be utilized.

The exemplary IOL 10 also includes one or more fixation members 1 and 2(e.g., haptics) that can facilitate its placement in the eye.

In this embodiment, each of the anterior and the posterior surfacesincludes a convex base profile, though in other embodiments concave orflat base profiles can be employed. While the profile of the posteriorsurface is defined solely by a base profile, the profile of the anteriorsurface is defined by addition of an auxiliary profile to its baseprofile so as to generate the aforementioned inner, outer and thetransition regions, as discussed further below. The base profiles of thetwo surfaces in combination with the index of refraction of the materialforming the optic can provide the optic with a nominal optical power.The nominal optical power can be defined as the monofocal refractivepower of a putative optic formed of the same material as the optic 12with the same base profiles for the anterior and the posterior surfacebut without the aforementioned auxiliary profile of the anteriorsurface. The nominal optical power of the optic can also be viewed asthe monofocal refractive power of the optic 12 for small apertures withdiameters less than the diameter of the central region of the anteriorsurface.

The auxiliary profile of the anterior surface can adjust this nominaloptical power such that the optic's actual optical power, ascharacterized, e.g. by a focal length corresponding to the axiallocation of the peak of a through-focus modulation transfer functioncalculated or measured for the optic at a design wavelength (e.g., 550nm), would deviate from the lens's nominal optical power, particularlyfor aperture (pupil) sizes in an intermediate range, as discussedfurther below. In many embodiments, this shift in the optical power isdesigned to improve near vision for intermediate pupil sizes. In somecases, the nominal optical power of the optic can be in a range of about−15 D to about +50 D, and preferably in a range of about 6 D to about 34D. Further, in some cases, the shift caused by the auxiliary profile ofthe anterior surface to the optic's nominal power can be in a range ofabout 0.25 D to about 2.5 D.

With continued reference to FIGS. 1A and 1B, the transition region 22 isin the form of an annular region that extends radially from an innerradial boundary (IB) (which in this case corresponds to an outer radialboundary of the inner refractive region 18) to an outer radial boundary(OB) (which in this case corresponds to inner radial boundary of theouter refractive region). While in some cases, one or both boundariescan include a discontinuity in the anterior surface profile (e.g., astep), in many embodiments the anterior surface profile is continuous atthe boundaries, though a radial derivative of the profile (that is, therate of change of the surface sag as a function of radial distance fromthe optical axis) can exhibit a discontinuity at each boundary. In somecases, the annular width of the transition region can be in a range ofabout 0.75 mm to about 2.5 mm. In some cases, the ratio of an annularwidth of the transition region relative to the radial diameter of theanterior surface can be in a range of about 0 to about 0.2.

In many embodiments, the transition region 22 of the anterior surface 14can be shaped such that a phase of radiation incident thereon would varymonotonically from its inner boundary (IB) to its outer boundary (OB).That is, a non-zero phase difference between the outer region and theinner region would be achieved via a progressive increase or aprogressive decrease of the phase as a function of increasing radialdistance from the optical axis across the transition region. In someembodiments, the transition region can include plateau portions,interspersed between portions of progressive increase or decrease of thephase, in which the phase can remain substantially constant.

In many embodiments, the transition region is configured such that thephase shift between two parallel rays, one of which is incident on theouter boundary of the transition region and the other is incident on theinner boundary of the transition region, can be a non-integer rationalfraction of a design wavelength (e.g., a design wavelength of 550 nm).By way of example, such a phase shift can be defined in accordance withthe following relation:

$\begin{matrix}{{{{Phase}\mspace{14mu}{shift}} = {\frac{2\pi}{\lambda}{OPD}}},} & {{Eq}.\mspace{14mu}\left( {1A} \right)} \\{{OPD} = {\left( {A + B} \right)\lambda}} & {{Eq}.\mspace{14mu}\left( {1B} \right)}\end{matrix}$wherein,

A designates an integer,

B designates a non-integer rational fraction, and

λ designates a design wavelength (e.g., 550 nm).

By way of example, the total phase shift across the transition regioncan be

$\frac{\lambda}{2},\frac{\lambda}{3},$etc, where λ represents a design wavelength, e.g., 550 nm. In manyembodiments, the phase shift can be a periodic function of thewavelength of incident radiation, with a periodicity corresponding toone wavelength.

In many embodiments, the transition region can cause a distortion in thewavefront emerging from the optic in response to incident radiation(that is, the wavefront emerging from the posterior surface of theoptic) that can result in shifting the effective focusing power of thelens relative to its nominal power. Further, the distortion of thewavefront can enhance the optic's depth of focus for aperture diametersthat encompass the transition region, especially for intermediatediameter apertures, as discussed further below. For example, thetransition region can cause a phase shift between the wavefront emergingfrom the outer portion of the optic and that emerging from its innerportion. Such a phase shift can cause the radiation emerging fromoptic's outer portion to interfere with the radiation emerging from theoptic's inner portion at the location at which the radiation emergingfrom the optic's inner portion would focus, thus resulting in anenhanced depth-of-focus, e.g., as characterized by an asymmetric MTF(modulation transfer function) profile referenced to the peak MTF. Theterm “depth-of-focus” and “depth-of-field” can be used interchangeablyand are known and readily understood by those skilled in the art asreferring to the distances in the object and image spaces over which anacceptable image can be resolved. To the extent that any furtherexplanation may be needed, the depth-of-focus can refer to an amount ofdefocus relative to a peak of a through-focus modulation transferfunction (MTF) of the lens measured with a 3 mm aperture and greenlight, e.g., light having a wavelength of about 550 nm, at which the MTFexhibits a contrast level of at least about 15% at a spatial frequencyof about 50 lp/mm. Other definitions can also be applied and it shouldbe clear that depth of field can be influenced by many factorsincluding, for example, aperture size, chromatic content of the lightforming the image, and base power of the lens itself.

By way of further illustration, FIG. 2A schematically shows a fragmentof a wavefront generated by an anterior surface of an IOL according toan embodiment of the invention having a transition region between aninner portion and an outer portion of the surface, and a fragment of awavefront incident on that surface, and a reference spherical wavefront(depicted by dashed lines) that minimizes the RMS (root-mean-square)error of the actual wavefront. The transition region gives rise to aphase advancement of the wavefront (relative to that corresponding to aputative similar surface without the transition region) that leads tothe convergence of the wavefront at a focal plane in front of theretinal plane (in front of the nominal focal plane of the IOL in absenceof the transition region). FIG. 2B schematically shows another case inwhich the transition region gives rise to a phase delay of an incidentwavefront that leads to the convergence of the wavefront at a focalplane beyond the retinal plane (beyond the nominal focal plane of theIOL in absence of the transition region).

By way of illustration, in this implementation, the base profile of theanterior and/or the posterior surfaces can be defined by the followingrelation:

$\begin{matrix}{z_{base} = {\frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {f\left( {r^{2},r^{4},r^{6},\ldots}\mspace{14mu} \right)}}} & {{Eq}.\mspace{14mu}(2)}\end{matrix}$wherein,

c denotes the curvature of the profile,

k denotes the conic constant, and

wherein,

ƒ(r², r⁴, r⁶, . . . ) denotes a function containing higher ordercontributions to the base profile. By way of example, the function ƒ canbe defined by the following relation:ƒ(r ² , r ⁴ , r ⁶, . . . )=α₂ r ²+α₄ r ⁴+α₆ r ⁶+  Eq. (3)wherein,

a₂ is a second order deformation constant,

a₄ is a fourth order deformation constant, and

a₆ is a sixth order deformation constant. Additional higher order termscan also be included.

By way of example, in some embodiments, the parameter c can be in arange of about 0.0152 mm⁻¹ to about 0.0659 mm⁻¹, the parameter k can bein range of about −1162 to about −19, a₂ can be in a range of about−0.00032 mm⁻¹to about 0.0 mm⁻¹, a₄ can be in a range of about 0.0 mm⁻³to about −0.000053 (minus 5.3×10⁻⁵) mm⁻³, and a₆ can be in a range ofabout 0.0 mm⁻⁵ to about 0.000153 (1.53×10⁻⁴) mm⁻⁵.

The use of certain degree of asphericity in the anterior and/orposterior base profile as characterized, e.g., by the conic constant k,can ameliorate spherical aberration effects for large aperture sizes.For large aperture sizes, such asphericity can somewhat degreecounteract the optical effects of the transition region, thus leading toa shaper MTF. In some other embodiments, the base profile of one or bothsurfaces can be tonic (that is, it can exhibit different radii ofcurvatures along two orthogonal directions along the surface) toameliorate astigmatic aberrations.

As noted above, in this exemplary embodiment, the profile of theanterior surface 14 can be defined by superposition of a base profile,such as the profile defined by the above Equation (1), and an auxiliaryprofile. In this implementation, the auxiliary profile (Z_(aux)) can bedefined by the following relation:

$\begin{matrix}{Z_{{aux}\;} = \left\{ \begin{matrix}{0,} & {0 \leq r < r_{1}} \\{{\frac{\Delta}{\left( {r_{2} - r_{1}}\; \right)}\left( {r - r_{1}} \right)},} & {r_{1} \leq r < r_{2}} \\{\Delta,} & {r_{2} < r}\end{matrix} \right.} & {{Eq}.\mspace{11mu}(4)}\end{matrix}$wherein,

r₁ denotes an inner radial boundary of the transition region,

r₂ denotes an outer radial boundary of the transition region, and

wherein,

Δ is defined by the following relation:

$\begin{matrix}{{\Delta = \frac{\alpha\;\lambda}{\left( {n_{2} - n_{1}} \right)}},} & {{Eq}.\mspace{14mu}(5)}\end{matrix}$wherein,

n₁ denotes an index of refraction of material forming the optic,

n₂ denotes an index of refraction of a medium surrounding the optic,

λ denotes a design wavelength, and

α denotes a non-integer fraction, e.g., ½.

In other words, in this embodiment, the profile of the anterior surface(Z_(sag)) is defined by a superposition of the base profile (Z_(base))and the auxiliary profile (Z_(aux)) as defined below, and shownschematically in FIG. 3:Z _(sag) =Z _(base) +Z _(aux)  Eq. (6)

In this embodiment, the auxiliary profile defined by the above relations(4) and (5) is characterized by a substantially linear phase shiftacross the transition region. More specifically, the auxiliary profileprovides a phase shift that increases linearly from the inner boundaryof the transition region to its outer boundary with the optical pathdifference between the inner and the outer boundaries corresponding to anon-integer fraction of the design wavelength.

In many embodiments, a lens according to the teachings of the invention,such the above lens 10, can provide good far vision performance byeffectively functioning as a monofocal lens without the optical effectscaused by the phase shift for small pupil diameters that fall within thediameter of the lens's central region (e.g., for a pupil diameter of 2mm). For medium pupil diameters (e.g., for pupil diameters in a range ofabout 2 mm to about 4 mm (e.g., a pupil diameter of about 3 mm)), theoptical effects caused by the phase shift (e.g., changes in thewavefront exiting the lens) can lead to enhanced functional near andintermediate vision. For large pupil diameters (e.g., for pupildiameters in a range of about 4 mm to about 5 mm), the lens can againprovide good far vision performance as the phase shift would onlyaccount for a small fraction of the anterior surface portion that isexposed to incident light.

By way of illustration, FIG. 4A-4C show optical performance of ahypothetical lens according to an embodiment of the invention fordifferent pupil sizes. The lens was assumed to have an anterior surfacedefined by the above relation (6), and a posterior surface characterizedby a smooth convex base profile (e.g., one defined by that aboverelation (2)). Further, the lens was assumed to have a diameter of 6 mmwith the transition region extending between an inner boundary having adiameter of about 2.2 mm to an outer boundary having a diameter of about2.6 mm. The base curvatures of the anterior and the posterior surfacewere selected such that the optic would provide a nominal optical powerof 21 D. Further, the medium surrounding the lens was assumed to have anindex of refraction of about 1.336. Tables 1A-1C below list the variousparameters of the lens's optic as well as those of its anterior andposterior surfaces:

TABLE 1A Optic Central Thickness Diameter (mm) (mm) Index of Refraction0.64 6 1.5418

TABLE 1B Anterior Surface Base Profile Base Conic Radius ConstantAuxiliary Profile (mm) (k) a₂ a₄ a₆ r1 r2 Δ 18.93 −43.56 0 2.97E−4−2.3E−5 1.1 1.25 −1.18

TABLE 1C Posterior Surface Base Radius (mm) Conic Constant (k) a₂ a₄ a₆−20.23 0 0 0 0

More specifically, in each of the FIGS. 4A-4C, through-focus modulationtransfer (MTF) plots corresponding to the following modulationfrequencies are provided: 25 lp/mm, 50 lp/mm, 75 lp/mm, and 100 lp/mm.The MTF shown in FIG. 4A for a pupil diameter of about 2 mm indicatesthat the lens provides good optical performance, e.g., for outdooractivities, with a depth-of focus of about 0.7 D, which is symmetricabout the focal plane. For a pupil diameter of 3 mm, each of the MTFsshown in FIG. 4B is asymmetric relative to the lens's focal plane (i.e.,relative to zero defocus) with a shift in its peak in the negativedefocus direction. Such a shift can provide a degree ofpseudoaccommodation to facilitate near vision (e.g., for reading).Further, these MTFs have greater widths than those shown by the MTFscalculated for a 2-mm pupil diameter, which translates to betterperformance for intermediate vision. For a larger pupil diameter of 4 mm(FIG. 4C), the asymmetry and the widths of the MTFs diminish relative tothose calculated for a 3-mm diameter. This in turn indicates good farvision performance under low light conditions, e.g., for night driving.

The optical effect of the phase shift can be modulated by varyingvarious parameters associated with that region, such as, its radialextent and the rate at which it imparts phase shift to incident light.By way of example, the transition region defined by the above relation(3) exhibits a slope defined by

$\frac{\Delta}{\left( {r_{2} - r_{1}} \right)},$which can be varied so as to adjust the performance of an optic havingsuch a transition region on a surface thereof, particularly forintermediate pupil sizes.

By way of illustration, FIGS. 5A-5F show calculated through-focusmodulation transfer function (MTF) at a pupil size of 3 mm and for amodulation frequency of 50 lp/mm for hypothetical lenses having ananterior surface exhibiting the surface profile shown in FIG. 3 as asuperposition of a base profile defined by the relation (2) and anauxiliary profile defined by the relations (4) and (5). The optic wasassumed to be formed of a material having an index of refraction of1.554. Further, the base curvature of the anterior surface and that ofthe posterior surface were selected such that the optic would have anominal optical power of about 21 D.

By way of providing a reference from which the optical effects of thetransition region can be more readily understood, FIG. 5A shows an MTFfor an optic having a vanishing Δz , that is, an optic that lacks aphase shift according to the teachings of the invention. Such aconventional optic having smooth anterior and posterior surfacesexhibits an MTF curve that is symmetrically disposed about the optic'sfocal plane and exhibits a depth of focus of about 0.4 D. In contrast,FIG. 5B shows an MTF for an optic according to an embodiment of theinvention in which the anterior surface includes a transition regioncharacterized by a radial extent of about 0.01 mm and Δz=1 micron. TheMTF plot shown in FIG. 5B exhibits a greater depth of focus of about 1D, indicating that the optic provides an enhanced depth of field.Further, it is asymmetric relative to the optic's focal plane. In fact,the peak of this MTF plot is closer to the optic than its focal plane.This provides an effective optical power increase to facilitate nearreading.

As the transition region becomes steeper (its radial extent remainsfixed at 0.01 mm) so as to provide a ΔZ=1.5 microns (FIG. 5C), the MTFbroadens further (that is, the optic provides a greater depth-of-field)and its peak shifts farther away from the optic than the optic's focalplane. As shown in FIG. 5D, the MTF for an optic having a transitionregion characterized by a ΔZ=2.5 microns is identical to the one shownin FIG. 5A for an optic having a ΔZ=0.

In fact, the MTF pattern is repeated for every design wavelength. By wayof example, in an embodiment in which the design wavelength is 550 nmand the optic is formed of Acrysof material (cross-linked copolymer of2-phenylethyl acrylate and 2-phenylethyl methacrylate) ΔZ=2.5 microns.For example, the MTF curve shown in FIG. 5E corresponding to a ΔZ=3.5microns is identical to that shown in FIG. 5B for a ΔZ=1.5, and the MTFcurve shown in FIG. 5F corresponding to a ΔZ=4 microns is identical tothe MTF curve shown in FIG. 5C corresponding to a ΔZ=1.5 microns. Theoptical path difference (OPD) corresponding to ΔZ for Z_(aux) defined bythe above relation (3) can be defined by the following relation:Optical Path Difference (OPD)=(n ₂ −n ₁)ΔZ  Eq. (7)wherein

n₁ represent the index of refraction of the material from which theoptic is formed, and

n₂ represents the index of refraction of the material surrounding theoptic. Thus, for n₂=1.552, and n₁=1.336, and a ΔZ of 2.5 microns, an OPDcorresponding to 1 λ is achieved for a design wavelength of about 550nm. In other words, the exemplary MTF plots shown in FIGS. 5A-5F arerepeated for a ΔZ variation corresponding to 1 λ OPD.

A transition region according to the teachings of the invention can beimplemented in a variety of ways, and is not restricted to the aboveexemplary region that is defined by the relation (4). Further, while insome cases the transition region comprises a smoothly varying surfaceportion, in other cases it can be formed by a plurality of surfacesegments separated from one another by one or more steps.

FIG. 6 schematically depicts an IOL 24 according to another embodimentof the invention that includes an optic 26 having an anterior surface 28and a posterior surface 30. Similar to the previous embodiment, theprofile of the anterior surface can be characterized as thesuperposition of a base profile and an auxiliary profile, albeit onethat is different from the auxiliary profile described above inconnection with the previous embodiment.

As shown schematically in FIG. 7, the profile (Z_(sag)) of the anteriorsurface 28 of the above IOL 24 is formed by superposition of a baseprofile (Z_(base)) and an auxiliary profile (Z_(aux)). Morespecifically, in this implementation, the profile of the anteriorsurface 28 can be defined by the above relation (6), which is reproducedbelow:Z _(sag) =Z _(base) +Z _(aux)wherein the base profile (Z_(base)) can be defined in accordance withthe above relation (2). The auxiliary profile (Z_(aux)) is, however,defined by the following relation:

$\begin{matrix}{z_{aux} = \left\{ \begin{matrix}{0,} & {0 \leq r < r_{1a}} \\{{\frac{\Delta_{1}}{\left( {r_{1b} - r_{1a}} \right)}\left( {r - r_{1a}} \right)},} & {r_{1a} \leq r < r_{1b}} \\{\Delta_{1},} & {r_{1b} \leq r < r_{2a}} \\{{\Delta_{1} + {\frac{\left( {\Delta_{2} - \Delta_{1}} \right)}{\left( {r_{2b} - r_{2a}} \right)}\left( {r - r_{2a}} \right)}},} & {r_{2a} \leq r < r_{2b}} \\\Delta_{2} & {r_{2b} < r}\end{matrix} \right.} & {{Eq}.\mspace{14mu}(8)}\end{matrix}$wherein r denotes the radial distance from an optical axis of the lens,and parameters r_(1a), r_(1b), r_(2a) and r_(2b) are depicted in FIG. 7,and are defined as follows:

r_(1a) denotes the inner radius of a first substantially linear portionof the transition region of the auxiliary profile,

r_(1b) denotes the outer radius of the first linear portion,

r_(2a) denotes the inner radius of a second substantially linear portionof the transition region of the auxiliary profile, and

r_(2b) denotes the outer radius of the second linear portion, andwherein each of Δ₁ and Δ₂ can be defined in accordance with the aboverelation (8).

With continued reference to FIG. 7, in this embodiment, the auxiliaryprofile Z_(aux) includes flat central and outer regions 32 and 34 and atwo-step transition 36 that connects the central and the outer regions.More specifically, the transition region 36 includes a linearly varyingportion 36 a, which extends from an outer radial boundary of the centralregion 32 to a plateau region 36 b (it extends from a radial locationr_(1a) to another radial location r_(1b)). The plateau region 36 b inturn extends from the radial location r_(1b) to a radial location r_(2a)at which it connects to another linearly varying portion 36 c, whichextends radially outwardly to the outer region 34 at a radial locationr_(2b). The linearly varying portions 36 a and 36 c of the transitionregion can have similar or different slopes. In many implementations,the total phase shift provided across the two transition regions is anon-integer fraction of a design wavelength (e.g., 550 nm).

The profile of the posterior surface 30 can be defined by the aboverelation (2) for Z_(base) with appropriate choices of the variousparameters, including the radius of curvature c. The radius curvature ofthe base profile of the anterior surface together with the curvature ofthe posterior surface, as well as the index of refraction of thematerial forming the lens, provides the lens with a nominal refractiveoptical power, e.g., an optical power in a range of about −15 D to about+50 D, or in a range of about 6 D to about 34 D, or in a rang of about16 D to about 25 D.

The exemplary IOL 24 can provide a number of advantages. For example, itcan provide sharp far vision for small pupil sizes with the opticaleffects of the two-step transition region contributing to theenhancement of functional near and intermediate vision. Further, in manyimplementations, the IOL provides good far vision performance for largepupil sizes. By way of illustration, FIG. 8 shows through-focus MTFplots at different pupil sizes calculated for a hypothetical opticaccording to an embodiment of the invention having an anterior surfacewhose profile is defined by the above relation (2) with the auxiliaryprofile of the anterior surface defined by the above relation (8) and asmooth convex posterior surface. The MTF plots are computed formonochromatic incident radiation having a wavelength of 550 nm . Tables2A-2C below provide the parameters of the anterior and the posteriorsurfaces of the optic:

TABLE 2A Optic Central Thickness Diameter (mm) (mm) Index of Refraction0.64 6 1.5418

TABLE 2B Anterior Surface Base Profile Base Auxiliary Profile RadiusConic r_(1a) r_(1b) r_(2a) r_(2b) Δ₁ Δ₂ (mm) Constant a₂ a₄ a₆ (mm) (mm)(mm) (mm) (micron) (micron) 18.93 −43.564 0 2.97E−4 −2.3E−5 1.0 1.011.25 1.26 0.67 2.67

TABLE 2C Posterior Surface Base Radius (mm) Conic Constant (k) a₂ a₄ a₆−20.23 0 0 0 0

The MTF plots show that for a pupil diameter of about 2 mm, which isequal to the diameter of the central portion of the anterior surface,the optic provides a monofocal refractive power and exhibits arelatively small depth of focus (defined as full width at half maximum)of about 0.5 D. In other words, it provides good far vision performance.As the pupil size increases to about 3 mm, the optical effects of thetransition region become evident in the through-focus MTF. Inparticular, the 3-mm MTF is significantly broader than the 2-mm MTF,indicating an enhancement in the depth-of-field.

With continued reference to FIG. 8, as the pupil diameter increases evenfurther to about 4 mm the incident light rays encounter not only thecentral and the transition regions but also part of the outer region ofthe anterior surface.

A variety of techniques and materials can be employed to fabricate theIOLs of the invention. For example, the optic of an IOL of the inventioncan be formed of a variety of biocompatible polymeric materials. Somesuitable biocompatible materials include, without limitation, softacrylic polymers, hydrogel, polymethymethacrylate, polysulfone,polystyrene, cellulose, acetate butyrate, or other biocompatiblematerials. By way of example, in one embodiment, the optic is formed ofa soft acrylic polymer (cross-linked copolymer of 2-phenylethyl acrylateand 2-phenylethyl methacrylate) commonly known as Acrysof. The fixationmembers (haptics) of the IOLs can also be formed of suitablebiocompatible materials, such as those discussed above. While in somecases, the optic and the fixation members of an IOL can be fabricated asan integral unit, in other cases they can be formed separately andjoined together utilizing techniques known in the art.

A variety of fabrication techniques known in the art, such as a casting,can be utilized for fabricating the IOLs. In some cases, the fabricationtechniques disclosed in pending patent application entitled “LensSurface With Combined Diffractive, Toric and Aspheric Components,” filedon Dec. 21, 2007 and having a Ser. No. 11/963,098 can be employed toimpart desired profiles to the anterior and posterior surfaces of theIOL.

Those having ordinary skill in the art will appreciate that variouschanges can be made to the above embodiments without departing from thescope of the invention.

The invention claimed is:
 1. A monofocal intraocular lens, comprising:an optic having an anterior surface and a posterior surface disposedabout an optical axis, at least one of said surfaces being toric and atleast one of said surfaces comprising: at least one inner refractiveregion having a nominal optical power, at least one outer refractiveregion having the nominal optical power, and a refractive transitionregion disposed between said inner and outer regions, said transitionregion extending from an inner radial boundary to an outer radialboundary thereof, wherein said transition region is adapted such that aphase of radiation incident thereon varies linearly over at least aportion of the radial extent between said inner to said outer boundaryso as to generate a phase shift between said outer and inner boundariescharacterized by a selected non-integer fraction of a design wavelengthin the visible spectrum such that a first portion of an incomingwavefront in the inner refractive region and a second portion of theincoming wavefront in the outer refractive region converge to produce aneffective optical power different from the nominal optical power therebycreating a depth of focus.
 2. The intraocular lens of claim 1, whereinthe transition region is adapted to provide a monotonic change inoptical path difference relative to the outer boundary of the innerregion as a function of increasing radial distance from the opticalaxis.
 3. The intraocular lens of claim 2, wherein the monotonic changeis characterized by a linear change in surface height Z_(tps) relativeto a refractive surface defining the nominal optical power as follows:$Z_{{tps}\;} = \left\{ \begin{matrix}{0,} & {0 \leq r < r_{1}} \\{{\frac{\Delta}{\left( {r_{2} - r_{1}} \right)}\left( {r - r_{1}} \right)},} & {r_{1} \leq r < r_{2}} \\{\Delta,} & {r_{2} < r}\end{matrix} \right.$ wherein, r₁ denotes an inner radial boundary ofthe transition region, r₂ denotes an outer radial boundary of thetransition region, and wherein, Δ is defined by the following relation:${\Delta = \frac{\alpha\lambda}{\left( {n_{2} - n_{1}} \right)}},$wherein, n₁ denotes an index of refraction of material forming theoptic, n₂ denotes an index of refraction of a medium surrounding theoptic when positioned for use in or on an eye, λ denotes the designwavelength, and α denotes the selected non-integer fraction.
 4. Theintraocular lens of claim 2, wherein the monotonic change ischaracterized by a succession of linear changes separated by one or moreplateaus and wherein a change in surface height z_(aux) relative to arefractive surface defining the nominal optical power is as follows:$z_{aux} = \left\{ \begin{matrix}{0,} & {0 \leq r < r_{1a}} \\{{\frac{\Delta_{1}}{\left( {r_{1b} - r_{1a}} \right)}\left( {r - r_{1a}} \right)},} & {r_{1a} \leq r < r_{1b}} \\{\Delta_{1},} & {r_{1b} \leq r < r_{2a}} \\{{\Delta_{1} + {\frac{\left( {\Delta_{2} - \Delta_{1\;}} \right)}{\left( {r_{2b} - r_{2a}} \right)}\left( {r - r_{2a}} \right)}},} & {r_{2a} \leq r < r_{2b}} \\\Delta_{2} & {r_{2b} < r}\end{matrix} \right.$ wherein r denotes the radial distance from anoptical axis of the lens, r_(1a) denotes a radius of a firstsubstantially linear portion of the transition region, r_(1b) denotesthe outer radius of the first linear portion, r_(2a) denotes an innerradius of a second substantially linear portion of the transitionregion, and r_(2b) denotes an outer radius of the second substantiallylinear portion., and wherein each of Δ₁ and Δ₂ can is defined inaccordance with the following relation:${\Delta_{1} = \frac{\alpha_{1}\lambda}{\left( {n_{2} - n_{1}} \right)}},{and}$$\Delta_{2} = \frac{\alpha_{2}\lambda}{\left( {n_{2} - n_{1}} \right)}$wherein, n1 denotes an index of refraction of material forming theoptic, n2 denotes an index of refraction of a medium surrounding theoptic, λ denotes the design wavelength, α₁ denotes a first non-integerfraction, and α₂ denotes a second non-integer fraction, the sum of thefirst and second non-integer fractions being the selected non-integerfraction.
 5. The intraocular lens of claim 1, wherein the selectednon-integer fraction is less than one.
 6. The intraocular lens of claim1, wherein the selected non-integer fraction is greater than one.
 7. Theintraocular lens of claim 1, wherein said transition region comprises anannular region.
 8. The intraocular lens of claim 7, wherein the annularregion has a radial width less than about 1 mm.
 9. The intraocular lensof claim 1, wherein at least one of the at least one surfaces has aradial diameter in a range of about 1 mm to about 5 mm.
 10. Theintraocular lens of claim 1, wherein said design wavelength is about 550nm.
 11. The intraocular lens of claim 1, wherein the optic exhibits athrough-focus modulation transfer function that is asymmetric relativeto a focal plane of said optic for at least a portion of a range ofaperture sizes between about 1.5 mm to about 6 mm.
 12. The intraocularlens of claim 1, wherein the effective optical power is characterized bya peak of a through-focus modulation transfer function of the optic atthe design wavelength for an aperture size in a range between about 1.5mm and 6 mm.
 13. The ophthalmic lens of claim 12, wherein the depth offield is characterized as a full width at 15% contrast level in thethrough-focus modulation transfer function.
 14. The ophthalmic lens ofclaim 1, wherein a difference of the effective power relative to thenominal optical power is between about 0.25 D and 1.75 D.